> How your thought operates to produce such a publicly testable result varies quite a bit, but visualization is one mode that is used by many people, but not exclusively.

I would say by most people capable of mathematics. Mathematics wouldn't even exist without it (visualization) in my opinion. But, is visualization the method or the product? You seem to claim it is the method. Can you give me an example of how, in your mind, you arrived at the proof you spoke of by "visualizing"? I would think that at some point you would have to associate abstract qualities to these images in order to make any comparisons, since you didn't have a picture to actually measure. For example, if I asked you if two equally sized circles can intersect at more than two points (forgetting the case where they are one and the same) you would, beyond picturing the event in your mind, have to develop some circle theory to reply with some certainty.